How to measure the density of a white dwarf if its diameter is 1000 km and weighs 10³⁰ kg?

Well, first of all, 10³⁰ kg is its mass, not its weight.

-- Density of anything is (its mass) divided by (its volume).

-- You know the white dwarf's mass.

-- The volume of any sphere is  (4/3) (pi) (radius)³

-- The radius is  1/2  of the diameter.

--  Now you have the ball.  Run with it.

I did it quickly and got  (1.91 x 10¹²) kilogram/meter³ .
That may be wrong.  You have to check it.  And even
if it's correct, you probably want to express density in
units of gram/cm³ the way everybody always does.